Question

Choose the correct answer of the following question:

A ladder makes an angle of 60° with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder is

(a) $\frac{4}{\sqrt{3}}$ m (b) $4\sqrt{3}$ m (c) $2\sqrt{2}$ m (d) 4 m [CBSE 2014]

Answer 1

Let AB be the wall and AC be the ladder.

We have,

$$\begin{gathered} \mathrm{BC}=2\mathrm{m}\mathrm{and}\angle \mathrm{ACB}=60° \\ \mathrm{In}∆\mathrm{ABC}, \\ \cos 60°=\frac{\mathrm{BC}}{\mathrm{AC}} \\ \Rightarrow \frac{1}{2}=\frac{2}{\mathrm{AC}} \\ \therefore \mathrm{AC}=4\mathrm{m} \end{gathered}$$

Hence, the correct answer is option (d).